Question

The New York Choral Society divides male singers up into four categories from highest voices to lowest: Tenor1, Tenor2, Bass1, Bass2. In the table are heights of the men in the Tenor1 and Bass2 groups. One suspects that taller men will have lower voices, and that the variance of height may go up with the lower voices as well. Do we have good evidence that the variance of the heights of singers in each of these two groups (Tenor1 and Bass2) are different?

Tenor1	Bass2	Tenor1	Bass2	Tenor1	Bass2
69	72	67	72	68	67
72	75	70	74	67	70
71	67	65	70	64	70
66	75	72	66		69
76	74	70	68		72
74	72	68	75		71
71	72	64	68		74
66	74	73	70		75
68	72	66	72

Short answer

According to the results, the P-value is $.34$.So, at$5\%$ level of significance null hypothesis will be accepted. So the height of Tenor 1 and the Bass 2 singers are not different variances.

Step-by-step solution

Step-1 Given Information

The New York Choral Society divides male singers up into four categories from highest voices to lowest: Tenor1, Tenor2, Bass1, Bass2

Step-2 Explanation

Consider the following data to check the variance of the heights of the singers in each of the two groups are different:

Tenor1	Bass2	Tenor1	Bass2	Tenor1	Bass2
69	72	67	72	68	67
72	75	70	74	67	70
71	67	65	70	64	70
66	75	72	66		69
76	74	70	68		72
74	72	68	75		71
71	72	64	68		74
66	74	73	70		75
68	72	66	72

Consider the null hypothesis that there is no significance difference between the variance two groups. For this, use Ti-83 calculator. Click on STAT $\to$ENTER, and then put the data into the list $L1,L2$. The screenshot is given as below:

Now again press STAT $\to$arrow over the TESTS $\to$arrow down to 2 sample F-test $\to$Select data and press then select1 and press var then select 2 in list 1 and list 2. And select the hypothesis as${\sigma }_{1}notequalto{\sigma }_2$ . The screen shot is given as below:

The screenshot of output is given below:

According to the above results, the P-value is $0.34$.So, at$5\%$level of significance null hypothesis will be accepted. So the height of Tenor 1 and the Bass 2 singers are not different variances.